Supplementary Text

Here are notes on selected topics that we decided not to include in the print version of our textbook. Instructors who have adopted the book for courses may wish to consider assigning student projects based upon some of the following.

1. Index Theory: Click HERE for notes on index theory in two dimensions and its relation to the dynamics of planar systems of ODEs. These notes may be regarded as an additional appendix for Chapter 7 of the main text. For an index-theory based solution of Chapter 7, Problem 9(d), visit the Hints and Solutions page.

2. Supplement to Appendix C.3: Click HERE for a sketch of the proof of the formula on page 520 in the main text (regarding the dependence of an eigenvalue lambda on the parameter epsilon).

Color Figures

Certain versions of our book were printed in black-and-white. Below are color versions of figures, which incorporate conventions that we adopted throughout the text. Most notably, stable manifolds are sketched in blue, unstable manifolds in red, center manifolds in purple, periodic orbits in green, homoclinic and heteroclinic orbits in purple, x-nullclines in brown, and y-nullclines in cyan.

Chapters 1-6 Chapters 7-8 Chapters 9-10
Figure 1.1 Figure 7.2 Figure 9.1
Figure 1.7 Figure 7.3 Figure 9.2
Figure 3.2 Figure 7.4 Figure 9.3
Figure 4.5 Figure 7.6 Figure 9.4
Figure 4.6 Figure 7.7 Figure 9.5
Figure 4.7 Figure 7.9 Figure 9.6
Figure 4.8 Figure 7.15 Figure 9.7
Figure 4.9 Figure 7.16 Figure 9.8
Figure 4.10 Figure 7.17 Figure 9.9
Figure 5.3 Figure 7.21 Figure 9.14
Figure 6.1 Figure 8.15 Figure 9.15
Figure 6.4 Figure 8.16 Figure 9.16
Figure 6.7 Figure 8.18 Figure 9.17
Figure 6.9 Figure 8.19 Figure 9.18
Figure 6.10 Figure 8.20 Figure 9.19
Figure 6.11 Figure 9.20
Figure 6.12 Figure 9.22
Figure 6.13 Figure 10.8
Figure 6.14 Figure 10.9
Figure 10.11
Figure 10.12